Chapter 5
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• As production volume changes, some costs may increase or decrease and other costs may remain stable.
• However, the predictability of specific costs to change with volume provides an important tool for managerial accountants.

Fixed costs stay the same in total.
They vary when expressed on a per unit basis.

Variable costs vary in direct proportion to volume changes.
They are constant when expressed as per unit amounts.

• The relevant range is the normal range of production that can be expected for a particular product and company.
• The relevant range can also be viewed as the volume of production for which the fixed and variable cost relationships hold true.

The concept of the relevant range allows managerial accountants to assume a linear cost relationship.

Some costs vary but only with relatively large changes in production volume. Costs like these are sometimes referred to as step costs .
Although step costs are technically not fixed costs, they may be treated as such if they remain constant within a relatively wide range of production.

Lets take an example of janitorial services within a company. As long as production is below 7,500 desks, the company will hire one janitor with salary and fringe benefits totaling $25,000. But if desk production exceeds
7,500, the company would hire a second janitor at a cost of another $25,000.
Production Janitors Cost
1 -7500 1 $25,000
7,501–15,000 2 $50,000

Expressing the link between costs and production volume as an algebraic equation is useful.
y = a + bx

If y = rent cost and x = units produced, y = $10,000 + $0x.
In this case, the y intercept is $10,000 and the slope is zero. In other words, fixed costs are $10,000 at any level of production within the relevant range.
Y
COSTS
$10,000
0
X
Fixed Costs
(RENT)
VOLUME

• Mixed costs have both a fixed and a variable component.
• They are costs that change in total and also change per unit.
• If you can’t draw a straight line through all the data points (below), then it is mixed .

• A variety of tools can be used to estimate the fixed and variable components of a mixed cost.
• One of those tools is regression analysis , which uses statistical methods to fit a cost line (called a regression line) through a number of data points.
• Regression analysis statistically finds the line that minimizes the sum of the squared distances from each data point to the line
(thus, sometimes called least squares regression).

Graphically, the line for the total overhead costs can be expressed as shown in the following illustration.

(Coefficient of Determination)
R-square is a measure of goodness of fit of the regression line (in fitting the data). An R 2 of 1.0
indicates a perfect correlation between the independent and dependent variables in the regression equation. In this case, R 2 of 0.8933 indicates that over 89 percent of the variation in overhead costs is explained by production.

Low R 2 may indicate:
(1) the chosen independent variable is not a very reliable predictor of the dependent variable;
(2) other independent variables may have an impact on the dependent variable; OR
(3) outliers or extreme observations are present.

Data points are:
High Activity = 2,600 Pizzas
(with $10,100 in overhead)
AND
Low Activity = 1,200 Pizzas
(with $6,750 in overhead)

Once the high and low volume points are identified, we begin the calculation for variable costs.
Variable Cost
Per Unit
=
=
=
Change in Cost
Change in Volume
$10,100 - $6,750
2,600 – 1,200
$2.39

We then solve for the fixed-cost component by calculating the total variable cost incurred at either the high or the low level of activity and subtracting the variable costs from the total overhead cost incurred at that level.
Total overhead
= Fixed costs + (Variable Number costs cost/unit
X of Pizzas)
$10,100 =
Fixed costs + ($2.39 X 2,600 Pizzas)
Fixed costs
= $3,886

The after-tax cost of a tax-deductible cash expenditure can be found by subtracting the income tax savings from the before-tax cost or by simply multiplying the before-tax amount by (1 - tax rate):
After-Tax
Cost
=
Pretax cost x (1- tax rate)

Similarly, the after-tax benefit of a taxable cash receipt can be found by subtracting the additional income tax to be paid from the before-tax receipt or by simply multiplying the pretax receipt by (1-tax rate):
After-Tax
Benefit
= Pretax receipts x (1- tax rate)

• Changes in production and inventory levels do not affect the calculation of profits.
• Variable costing focuses attention on relevant product costs rather than on fixed product costs, which are often unavoidable.
• Under variable costing, cost behavior is emphasized and fixed costs are separated from variable costs on the income statement.
• Variable costing is consistent with variance analysis.
• Variable costing income is more closely aligned with a company’s cash flows.